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From the TCDSB Mathematics Dept MENTAL MATH NOVEMBER 2014 Addition using Digits of Same Units What is Mental Math? • Mental math is often used as a way to calculate, estimate and/or visualize mathematical computations and relationships in one’s head. • Mental strategies were previously learned conceptually with and without the use of paper/pencil calculations and math tools. How would you determine the sum of these four 4 digit whole numbers (or 4 addends)? 3411 + 2324 + 4142 + 1233 • Would you add the first 2 numbers, then add on the 3rd number, followed by the 4th number? Or would you add the thousands, then hundreds, tens and ones? • If you know 3411 + 2324 + 4142 + 1233, does it help you to determine the sum for 34.11 + 23.24 + 41.42 + 12.33? • If you know 3411 + 2324 + 4142 + 1233, does it help you to determine the sum of 34.11 + .2324 + 414.2 + 1.233? Key Mathematical Idea • Whole number units for digits include ones, tens, hundreds, thousands, ten thousands … • Decimal number units for digits include tenths, hundredths, thousandths … • Addends are the number of numerals in an addition expression or equation. If you know that 1+2+3+4=10, then you know: • 1 + 2 + 3 + 4 = 10 ones = 10 • 10+20+30+40 = (1+2+3+4) tens = 10 tens = 100 ones • 100+200+300+400 = (1+2+3+4) hundreds = 10 hundreds = 100 tens = 1000 ones = 1000 • 1000+2000+3000+4000 = (1+2+3+4) thousands = 10 thousands = 100 hundreds = 1000 tens = 10 000 ones= 10 000 Sample - Grade 2 Learning Goal and Success Criteria Add 1 digit whole numbers, with 4 or more addends by using the commutative property for addition to make compatible numbers (2+3=5; 2, 3 are compatible numbers). • 1+3+4+2=1+4+3+2=5+5 =10 ones • 1+2+3+4+1+3+4+2 = 10 ones+10 ones = 1+1+2+2+3+3+4+4=double ten ones = 2+3+2+3+1+4+1+4 = 4 groups of 5 = 20 ones Possible Sequence of Mental Math Questions for 2 Digit # • 1+2+3+4 (change order then double addends (e.g., 1+2+3+4+1+2+3+4) • 10+20+30+40 (changer order, then double addends) • 11+22+33+44 (change order, then double addends) • 12+23+34+41 (change order of numeral, then change digits within numeral, then double addends) Create Mental Math Practise Questions Create addition questions, using (1 digit (ones); 2 digit (tens, ones), 3 digit (hundreds, tens, ones), 4 digit (thousands, hundreds, tens, ones) and so on. Numbers to use for: • grade 2 (1-digit; sum to 18) • grade 3 (2-digit or less) • grade 4 (3 digit or less) • grade 5 (4 digit or less) • grades 6 to 9 (any size digit number) As the next set of mental math challenges, start with 6+7+8+9 = 15+15 = 30 in place of 1+2+3+4 = 5+5 = 10 Helping Your Child Learn Mathematics AT HOME Developing a Growth Mindset for Loving and Learning Mathematics Jo Boaler identifies several norms that contribute to a positive and productive mathematics learning environment. Consider ways that these norms can be established in your home, a mathematics learning environment for your child. • Everyone can learn math to the highest levels. Students who have a growth mindset believe “that they can learn anything, and the more work they do the smarter they will get.” Students need to know that they can learn math and there is no such thing as a math person. • Mistakes are valuable. “Mistakes grow your brain! It is good to struggle and make mistakes.” • Questions are really important. Encourage your child to ask questions. (e.g., Why does that work? How does one strategy relate to another strategy?) • Math class is about learning not performing. “Math is a growth subject, it takes time to learn and it is all about effort.” November 2014